论文标题
关于非交通性Minkowski时空和探针奇异行为的非平板性质
On the Non-Flatness Nature of Noncommutative Minkowski Spacetime and the Singular Behavior of Probes
论文作者
论文摘要
Minkowski时空是平坦的，这不止一个世纪以上的概念。从纯粹的几何学角度来看，我们明确解决了一个非交流性的Minkowski时空的问题。 In the framework of the twisted-diffeomorphism approach to noncommutative gravity with canonical type noncommutative (NC) coordinate structure, one important result that we get is that the NC Minkowski spacetime parametrized either with spherical polar coordinates or with parabolic coordinates has nontrivial NC corrections to Riemann curvature tensor, Ricci tensor and curvature scalars.另一个至关重要的结果是，曲率标量在某些点具有奇异的行为，而这些奇异性不是坐标的奇异性。这些奇异性的性质显然指向高能探针变成黑洞的想法。在笛卡尔坐标和圆柱形坐标的情况下，没有任何此类非交易性校正，因此没有任何此类奇异性，这会得出这样的结论：当考虑到这些坐标的规范NC结构时，高能量探针不会变成黑洞。
It is more than a century-old concept that the Minkowski spacetime is flat. From the pure geometric point of view, we explicitly address the issue of whether a noncommutative Minkowski spacetime is flat or not. In the framework of the twisted-diffeomorphism approach to noncommutative gravity with canonical type noncommutative (NC) coordinate structure, one important result that we get is that the NC Minkowski spacetime parametrized either with spherical polar coordinates or with parabolic coordinates has nontrivial NC corrections to Riemann curvature tensor, Ricci tensor and curvature scalars. Another crucial result is that the curvature scalars have singular behavior at certain points, and these singularities are not coordinate singularities. The nature of these singularities clearly points towards the idea of high-energetic probes turning into black holes. The absence of any such noncommutative corrections, and thus any such singularities, in the cases of Cartesian coordinates and cylindrical coordinates leads to the conclusion that high-energetic probes do not turn into black holes when the canonical NC structure is considered for these coordinates.
